Iran or Persia- and Aryans!
The nomadic cattle-herders who settled there (around 1000 BC) and who still live there called themselves Aryans or Iranians. The name means "the nobles" or "the freemen". It's from the same original root as Eire and Ire-land. Another branch of the same people entered India at roughly the same time, and also called themselves "Aryans" - although they called their country "Bharat" (they still do). It's worth pointing out that the Indo-Iranians were a branch of the Indo-European peoples, who included the Greeks, the Romans, the ancestors of the Russians, the Celts, the Germans - and the English. DNA evidence (see David Reich, Who We Are and How We Got Here, Oxford 2018) indicated that Indo-European speakers, developed north of the Caucasus from a mixing of Iranian farmers and East Eurasian hunter gatherers who had mastered horse and cart technology as well as bronze. They are identified as the Yamnaya people, who moved into northern Europe, the Eurasian steppe, and the Indian subcontinent between 7 and 5 kya (thousand years ago), and, in northern Europe, including Britain, replaced around 90% of the earlier inhabitants (ie the builders of Stonehenge).
Wikipedia on "Aryans"
"Drawing on misinterpreted references in the Rig Veda by Western scholars in the 19th century, the term "Aryan" was adopted as a racial category through the works of Arthur de Gobineau, whose ideology of race was based on an idea of blonde northern European "Aryans" who had migrated across the world and founded all major civilizations, before being degraded through racial mixing with local populations. Through the works of Houston Stewart Chamberlain, Gobineau's ideas later influenced the Nazi racial ideology which saw "Aryan peoples" as innately superior to other putative racial groups.
The atrocities committed in the name of this racial ideology have led academics to avoid the term "Aryan", which has been replaced, in most cases, by "Indo-Iranian". The term now only appears in the context of the "Indo-Aryan languages"."
Iran/Persia is quite complicated!
Iranian is a name used to categorise various nomadic herding peoples who came from or still remained in the steppes of Central Asia. They include the Scythians, once dominant as far east as Siberia - and probably the Tocharians of the mountains and deserts north of Tibet. Around 1000 BC, several peoples began to move with their animals on to what's now called the Iranian plateau - they included the Medes, who were the first to build an empire for themselves after defeating the crumbling Assyrian empire in 612 BC. We don't really know how extensive this was. At the same time the Persians arrived, moving further south to the area known as Persis, between the southern Zagros and the Persian Gulf. As the Medes had to overcome the Assyrians, so the Persians overcame the Elamites. After the Persians under Cyrus, who was half Mede, established hegemony, the empire became the Persian empire (although Greeks continued to use the terms Mede and Persian indiscriminately!). The people known as Parthians (real name unknown) were an Iranian people who took over the "Persian" empire from the Macedonian (not really Greek!) successors of Alexander. The Sasanians who took over from them were Persians, in the sense that they came from Persis - but they divided their empire into Iran (home of Iranian speaking Mazda worshipping peoples) and Aniran (others).
The modern name normally used for the part of Iran where the Persians established themselves is FARS, hence the language FARSI. Many Iranians prefer to call it Pars and the language Persian. The F is only there because the Arabs have no P in their alphabet. It’s always difficult to get away from politics!
But in the west, thanks to the prestige of Greek and Roman writers who always referred to PERSIA, Persia was always used for everything connected with Iran, whether strictly Persian or not. The situation was remedied in 1920s, when Reza Shah officially changed the name to IRAN. Since the revolution in 1979, some exiles and opponents of the regime have taken to referring to the country as Persia. Politics again!
Actually few of us in the "UK" really understand the difference between the terms: The British Isles, Great Britain, The United Kingdom. Try it on your students. No wonder so many foreigners call us "England" - and what does "British" really mean?
The Rulers of Iran box is somewhat simplified - especially since the Arab conquest. Iran was ruled by Arabs from Damascus in Syria, until they were overcome by a rival dynasty of Arab caliphs (successors to Muhammad) - the Abbasids, who claimed actual descent from the prophet's family (His uncle Abbas in fact). Their descendants were accepted as caliphs until the Mongol destruction of Baghdad in 1258. But the caliphs - although recognised as heads of Islam, lost their actual political power to the Seljuq Turks, who invaded from the east. Much later, there was confusion as the Safavid dynasty declined - only Nader Shah briefly reasserted control, until Iran was stabilised under the Qajars. See the website for details.
The picture shows a ziggurat built by the Elamites, in western Iran, who were defeated/absorbed by the Persians. Their language - unrelated to any other known language - continued to be used for administration by the Persians.
More on the website: https://www.the-persians.co.uk/intro2.htm
Also (DNA) see https://www.the-persians.co.uk/beginnings.htm